IJPAM: Volume 106, No. 3 (2016)

A NEW OPTIMIZED RUNGE-KUTTA METHOD
FOR SOLVING OSCILLATORY PROBLEMS

Kasim Hussain$^1$, Fudziah Ismail$^2$, Norazak Senu$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA
$^1$Department of Mathematics
College of Science
Al-Mustansiriyah University
Baghdad, IRAQ
$^{2,3}$Institute for Mathematical Research
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA


Abstract. A new explicit Runge-Kutta method of fifth algebraic order is developed in this paper, for solving second-order ordinary differential equations with oscillatory solutions. The new method has zero phase-lag, zero amplification error and zero first derivative of the phase-lag. Numerical results show that the new proposed method is more efficient as compared with other Runge-Kutta methods in the scientific literature, for the numerical integration of oscillatory problems.

Received: October 25, 2015

AMS Subject Classification: 65L05, 65L06

Key Words and Phrases: Runge-Kutta method, phase lag, amplification error, oscillatory problems

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DOI: 10.12732/ijpam.v106i3.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 3
Pages: 715 - 726


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